I am not sure why its not A) 4 points because the question asks for point "ON" the circle. and there are only 4 points "On" the circle. (0,5) , (5,0) , (0,-5) and (-5,0)

ILULA08 wrote:I am not sure why its not A) 4 points because the question asks for point "ON" the circle. and there are only 4 points "On" the circle. (0,5) , (5,0) , (0,-5) and (-5,0)

If the radius of the circle is 5, and the circle is centered on the origin (0,0) then any point that is 5 units from the origin will be on the circle. (3,4) for example is 5 units from the origin, and thus is on the circle.

For a visual:

Rastis wrote:but arent' there an infinite number of points on a circle? I am confused as to why those points are the only ones that are integers.

There are an infinite number of points on a circle. The problem specifies that it is interested only in the cases where x and y are integers.

So, knowing that x^2 + y^2 =5^2, TEST integer values of x, for example, 1,2,3,4,5 and solve for y to determine if it, too, is an integer. If so, then you have an x and y that are both integers.

So, x=2 yields x^2 = 4. 5^2 - 4 = 21, which must be y^2. The only y that would work lies between 4 and 5, therefore not an integer.

Following this reveals that only 5,0 and 3,4 and its negative variants work.

ILULA08 wrote:I am not sure why its not A) 4 points because the question asks for point "ON" the circle. and there are only 4 points "On" the circle. (0,5) , (5,0) , (0,-5) and (-5,0)

Be careful here - I think you're thinking of points that are both on the circle AND on one of the axes. We only want points on the circle, irrespective of the axes, so there are more than these four.